An airline pilot pulls her 12.0 kg rollaboard suitcase along the ground with a force of 25.0 N for 10.0 meters. The handle she pulls on makes an angle of 44.0 degrees with the horizontal. How much work does she do over the ten-meter distance?
To calculate the work done by the airline pilot, you can use the equation:
Work = Force * Distance * cos(theta)
Where:
- Work is the amount of work done (in joules, J)
- Force is the applied force (in newtons, N)
- Distance is the displacement (in meters, m)
- theta is the angle between the applied force and the direction of displacement (in degrees)
In this case, the applied force is 25.0 N, the distance is 10.0 meters, and the angle is 44.0 degrees. The first step is to convert the angle from degrees to radians:
theta_radians = theta * (pi/180)
theta_radians = 44.0 * (pi/180) = 0.7679 radians
Now, we can calculate the work:
Work = 25.0 N * 10.0 m * cos(0.7679 radians)
To calculate the cosine of 0.7679 radians, use a scientific calculator or mathematical software. The result is approximately 0.7225.
Work = 25.0 N * 10.0 m * 0.7225
Work = 180.625 J
Therefore, the airline pilot does approximately 180.625 joules of work over the ten-meter distance.
Fh = 25cos44 = 17.98N.
W = Fh*d = 17.98 * 10 = 179.8J.